Method for the manufacture of a spatially varying dielectric material, articles made by the method, and uses thereof

ABSTRACT

A stereolithography method of manufacture of a polymer structure having a spatially gradient dielectric constant, including: providing a volume of a liquid, radiation-curable composition; irradiating a portion of the liquid, radiation-curable composition with activating radiation in a pattern to form a layer of the polymer structure; contacting the layer with the liquid, radiation-curable composition; irradiating the liquid, radiation-curable composition with activating radiation in a pattern to form a second layer on the first layer; and repeating the contacting and irradiating to form the polymer structure, wherein the polymer structure comprises a plurality of unit cells wherein each unit cell is integrally connected with an adjacent unit cell, each unit cell is defined by a plurality of trusses formed by the irradiation, wherein the trusses are integrally connected with each other at their respective ends, and the trusses of each unit cell are dimensioned to provide the spatially gradient dielectric constant.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of application of Application No.17/855,999, filed Jul. 1, 2022, which is divisional application ofApplication No. 16/657,054, filed Oct. 18, 2019, now U.S. Pat. No.11,407,169, which claims priority to and the benefit of U.S. ProvisionalApplication 62/747,497 filed on Oct. 18, 2018, which are incorporatedherein by reference in their entirety.

BACKGROUND

Disclosed herein is method for the manufacture of structures having aspatially varying dielectric constant by additive manufacturing,electronic devices made by the method, and uses of the electronicdevices in electronic articles.

Numerous dielectric structures having a preselected dielectric constanthave been described for use in electronic devices. Methods for themanufacture of structures having a spatially varying dielectricconstant, such as a Luneburg lens, is a more difficult problem to solve.One method to approach manufacture of a structure such as a Luneburglens is to spatially vary the density of a dielectric material, whichgives rise to a corresponding spatial variance of dielectric constant.For example, US5677796 describes a Luneburg lens having a dielectricgradient formed by drilling a plurality of holes extending radially fromthe center of a sphere to control the resultant local density of thematerial, and thus the relative dielectric constant as a function of thedistance from the center of the sphere. US7179844 describesthree-dimensional expansion of three different composites to providethree different materials having a uniform, but different dielectricconstant, and then layering the materials to provide a structure havinga step gradient of the dielectric constants. These methods are slow,complex, and difficult to adapt to different shapes and differentgradients.

Additive manufacturing (AM) (which includes 3-dimensional (3D) printingand solid freeform fabrication) allows the production ofthree-dimensional objects of virtually any shape from a digital model.Generally, this is achieved by creating a digital blueprint of a desiredstructure with computer-aided design (CAD) modeling software and thenslicing that virtual blueprint into digital cross-sections. Thesecross-sections are formed or deposited in a sequential layering processto create the 3D structure. Liang et al. have described an additivemanufacturing (AM) method to make structures having a step gradient ofthe dielectric constants. (Liang, M. et al., “A 3-D Luneburg lensantenna fabricated by polymer jetting rapid prototyping,” IEEETransactions on Antennas and Propagation, 62(4), 1799-1807.) Liang etal. describe a polymer jetting process similar to an ink jetting processwhere thin layers of two different radiation curable compositions (onefor the object and one for a support material) are jetted onto a stageand cured. The polymer jetting process allows the manufacture of smallstructures of a varying overall shape. However, the shape is limited inthat no overhangs can be present unless a support material issimultaneously laid down and then removed. The process is furtherlimited with respect to the types of polymers used, as the polymer mustbe jettable in very fine streams, while at the same time providing thedesired mechanical and electrical characteristics upon cure.

There accordingly remains a need in the art for efficient, flexiblemethods for the manufacture of dielectric polymer structures that varyspatially in dielectric constant across the material.

BRIEF SUMMARY

Disclosed herein is a method for the manufacture of a polymer structurehaving a spatially gradient dielectric constant, the method comprising:providing a volume of a liquid, radiation-curable composition;irradiating a portion of the liquid, radiation-curable composition withactivating radiation in a pattern to form a layer of the polymerstructure; contacting the layer with the liquid, radiation-curablecomposition; irradiating the liquid, radiation-curable composition withactivating radiation in a pattern to form a second layer on the firstlayer; and repeating the contacting and irradiating to form the polymerstructure, wherein the polymer structure comprises a plurality of unitcells wherein each unit cell is integrally connected with an adjacentunit cell, each unit cell is defined by a plurality of trusses formed bythe irradiation, wherein the trusses are integrally connected with eachother at their respective ends, and the trusses of each unit cell aredimensioned to provide the spatially gradient dielectric constant.

The polymer structures made by the above method are also disclosed.

In another aspect, an electronic device comprises a polymer structure,wherein the polymer structure comprises: a unified body of a dielectricmaterial comprising a plurality of unit cells, each unit cell comprisinga plurality of trusses integrally connected with each other at theirrespective ends, wherein each unit cell is integrally connected with anadjacent one of the unit cells; and wherein the average dielectricconstant of the unified body of the dielectric material varies from afirst portion of the body to a second portion of the body.

Also described is an electronic device comprising the polymer structure,wherein the unified body of dielectric material forms at least part ofan impedance-matching layer, a dielectric waveguide, a lens, a reflectarray, an antenna matching structure, a superstrate, a coupler, adivider, or a dielectric antenna.

The above described and other features are exemplified by the followingfigures, detailed description, examples, and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The following Figures are exemplary aspects, which are provided toillustrate aspects of this disclosure.

FIG. 1A is a schematic, perspective view of a cubic lattice unit cell ofa polymer structure, and FIG. 1B is a schematic, perspective view of apolymer structure containing a plurality of cubic lattice unit cells asshown in FIG. 1A;

FIG. 2A is a schematic, perspective view of an octet lattice unit cellof a polymer structure and FIG. 2B is a schematic, perspective view of apolymer structure containing a plurality of octet lattice unit cells asshown in FIG. 2A;

FIG. 3A to FIG. 3F are schematic cross-sectional views of trusses ofexemplary embodiments;

FIG. 4A to FIG. 4D are schematic side views of trusses of exemplaryembodiments;

FIG. 5 is a graph showing Dk versus truss diameter for an octet unitcell;

FIG. 6A to FIG. 6J are schematic representations of shapes of thepolymer structure of exemplary embodiments;

FIG. 7A to FIG. 7E are schematic cross-sectional views of polymer shapesof exemplary embodiments;

FIG. 8 is a schematic, perspective view of a polymer structure having astep gradient dielectric constant increasing in the X-direction due toincreasing truss diameter in the X-direction;

FIG. 9 is a schematic, perspective view of a polymer structure having acontinuous gradient dielectric constant increasing in the X-directiondue to increasing truss diameter in the X-direction;

FIG. 10A to FIG. 10F are schematic representations of dielectricgradients of the polymer structures of exemplary embodiments; and

FIG. 11 depicts an electronic structure or device, in particular anelectromagnetic structure or device, in accordance with an embodiment.

DETAILED DESCRIPTION

It has been discovered by the inventors hereof that polymer structuresvarying in dielectric constant across the polymer material can beefficiently obtained using stereolithography apparatus (SLA) additivemanufacturing. In particular, SLA methods can be used to provide polymerstructures having an open-lattice cell structure wherein the size ofeach lattice is varied to provide a corresponding change in dielectricconstant. This method allows fast, efficient manufacture of structureshaving a preselected dielectric constant gradient in a variety ofconfigurations and a variety of shapes. The method is also amenable touse of different polymers and polymer compositions. Polymer structuresuseful in 5G applications can be manufactured.

SLA is also referred to in the art as optical fabrication,photosolidification, and resin printing. Any of the foregoing methodscan be used herein and are referred to collectively as “SLA” methods. Inthese methods, successive thin layers of a liquid resin are selectivelyphotopolymerized using a light source, starting from the bottom layer tothe top layer or starting from the top layer to the bottom layer. Thisprocess has been described, for example, in US4575330, US4929402,US5104592, US5184307, US5192559, US5234636, US5236637, and US5273691.

There are different approaches to SLA, including direct/laser writingand mask-based writing using digital projection. In direct/laser writinga stage on which the polymer material is formed is located just below asurface of a volume of a curable liquid resin composition for theformation of a polymer. A single light source (e.g., a laser) movesalong the surface of the curable composition, row by row, untilcompletely curing the desired layer. To initiate the following layer,the stage sinks lower into the volume of the curable liquid resincomposition until a new layer of the curable composition covers thesurface and the curing process repeats. In between layers, a bladeloaded with the curable liquid resin composition levels the surface ofthe resin to ensure a uniform layer of liquid prior to another round oflight exposure. This procedure repeats until the curable liquid resincomposition is printed to form the 3D structure.

In mask-based writing using digital projection, the stage is submerged adefined distance into the volume of the liquid, curable composition. Thevolume is located in a bath having an optically clear bottom. Next, thelight source is guided to the stage in a pattern to polymerize thecurable composition between the light source and the stage. In thedigital projection method, a digital mirror device allows an entirelayer of a given pattern to be cured simultaneously. The stage can thenbe raised by a defined distance, and another layer can be cured. Thisprocedure repeats until the curable liquid resin composition is printedto form the 3D structure.

The polymer structures formed by SLA are a unified body of dielectricmaterial that comprises a plurality of unit cells. Each unit cellcomprises a plurality of trusses integrally connected with each other attheir respective ends. Each unit cell is integrally connected with anadjacent one of the unit cells. The average dielectric constant of theunified body of dielectric material varies from one portion of the bodyto another portion of the body. For example, the average dielectricconstant of the unified body of dielectric material can vary from aninner portion of the body to an outer portion, or from one side of thebody to another side.

In particular, the unit cells comprise trusses that define interstitialspaces, as illustrated, for example, in FIG. 1A and FIG. 1B. FIG. 1Ashows a cubic unit cell 10 comprising trusses 12 defining interstitialspace 13. FIG. 2A shows an octet unit cell 20 comprising trusses andinterstitial spaces defined by the trusses. As used herein, the term“truss” means a structural member of a framework of the members, whereeach truss member is connected to another adjacent truss member only atits respective ends 14, as indicated by the spheres 14, to form jointsbetween truss ends. Any load distributed through each truss member isassumed to be distributed through the corresponding joints 14. It is tobe understood that the spheres shown at joints 14 are only forillustration of the joints and may or may not be present in the polymerlattice structures. In an aspect, no additional material is present atthe joints of the polymer lattice structures except the materialcontributed by each truss forming the joint.

Each truss 12 can be straight or curved. In an aspect, each truss issubstantially straight. Each truss can have a cross-section that isirregular or substantially regular. For example, with reference to FIGS.3B-3F, the cross-section can be circular (FIG. 3A), elliptical (FIG.3B), polygonal, e.g., hexagonal (FIG. 3C) or rectangular (3D), ring(FIG. 3E), ovoid (FIG. 3F), or the like. In an aspect, each truss is ofthe same cross section throughout the length of the truss, such ascircular or square. Alternatively, it is possible to vary thecross-section of each truss, for example having a truss that issubstantially circular at each end, but substantially square in theportion between each end. Each truss within a unit cell can further havethe same cross-sectional diameter, or a varying diameter. For example,while each truss 12 in FIG. 2A is shown as having a substantiallyuniform diameter throughout its length, with reference to FIGS. 4A-4D,each truss could have a diameter that varies along its length, forexample a dog bone shape (FIG. 4A) having a larger circular diameter ateach end thereof, or a pyramidal (FIG. 4B) or a polygonal shape (4C) oflarger diameter at each end thereof. In some aspects, particularly wherea continuous gradient is desired as described in more detail below, thetruss can have a continuously varying diameter from one end to the otherend, i.e., from smaller to larger (FIG. 4D) where H₁ is less than H₂.

Each truss can have a diameter in the range of 0.03 to 5.0 millimeters(mm), preferably 0.05 to 4.0 mm. “Diameter” as used herein refers to theaverage largest cross-sectional dimension. Where the truss has asubstantially constant diameter, the average diameter can be in therange of 0.03 to 5.0, preferably 0.05 to 4.0. Where the truss has acontinuously varying diameter, the truss can vary within this range, forexample from 0.03 to 1.0 mm, from 1.0 to 1.7 mm, from 1.7 to 2.4 mm, andso on.

The unit cells can be of any lattice configuration, for example cubic(FIG. 1A) and its variations, e.g., body-center cubic or face centercubic, or octet (FIG. 2A). Use of an octet lattice unit cell ispreferred, as it allows thinner truss diameters and lengths that can bemore easily scaled to higher frequencies. Octet lattice units are alsoadvantageous because they can have an isotropic dielectric constantwithin the unit, such that a given electromagnetic wave can interactwith the unit in the same way regardless of its orientation. Asimulation predicting dielectric constant (Dk) versus truss diameter inmillimeters is shown in FIG. 5 .

Each of the unit cells can have size less than 30%, or less than 20%, orless than 10% of a wavelength of an electromagnetic wave that thepolymer structure is designed to operate with. The wavelength of theelectromagnetic wave is limited primarily by manufacturing capabilities,and therefore can vary widely. In an aspect the frequency range ofoperation is 1 to 100 GHz, i.e., a wavelength of 3 to 300 mm. Thesmallest cell size (e.g., 1 mm) can presently be limited by currentmanufacturing capabilities.

As shown in FIGS. 1B and 2B, the polymer structure is a unified,three-dimensional body that includes a plurality of unit cells whereineach cell is adjacent to another cell. In an aspect each unit cell isintegrally connected with an adjacent one of the unit cells. Forexample, polymer structure 20 in FIG. 1B includes eight unit cells 10.While the polymer structures of FIGS. 1B and 2B are shown as a cube andan irregular shape, respectively, any shape can be used. With referencenow to FIGS. 6A-6J, any dielectric structure 20 disclosed herein canhave a three-dimensional form in the shape of a cylinder (FIG. 6A), apolygon box (FIG. 6B) a tapered polygon box (FIG. 6C), a cone (FIG. 6D),a cube (FIG. 6E), a truncated cone (FIG. 6F), a square pyramid (FIG.6G), a toroid (FIG. 6H), a dome (FIG. 6I), an elongated dome (FIG. 6J),or any other three-dimensional form suitable for a purpose disclosedherein. Referring now to FIGS. 7A-7E, such shapes can have a z-axiscross section in the shape of a circle FIG. (7A), a polygon (FIG. 7B), arectangle (FIG. 7C), a ring (FIG. 7D), an ellipsoid (FIG. 7E), or anyother shape suitable for a purpose disclosed herein. In addition, theshape can depend on the polymer used, the desired dielectric gradient,the selected type of unit cell, and the desired mechanical andelectrical properties.

The dielectric gradient in the polymer structure is established byvarying the density of each unit cell, more commonly the density of aselected set of unit cells. The density can be varied by including morematerial in each unit cell, where more material provides a higherdielectric constant and less material provides a lower dielectricconstant. For example, as disclosed in Liang et al., referenced above,each set of unit cells in a layer can contain additional polymerdeposited at the joint of the unit cell.

In a preferred aspect, the density of the polymer structure is varied byvarying the diameter of each truss in a selected set of unit cells.Referring to FIG. 8 , polymer structure 20 includes three sets of unitcells in the X-direction, 10 a, 10 b, and 10 c. The diameter of eachtruss of each of set of unit cells 10 a, 10 b, and 10 c increases inthickness in the X-direction, decreasing the size of the interstices 13a, 13 b, 13 c in each of unit cells 10 a, 10 b, and 10 c respectively.When the interstices are filled with air, a step gradient of dielectricconstants from lower (set 10 a) to higher (set 10 c) is provided.

In another aspect, the diameter of each truss of a unit cell can varywithin a set of cells to provide a continuous gradient. As shown forexample, in FIG. 9 , trusses 12 a along the X-direction (the horizontaltrusses) of set 10 a increase in diameter from end 14 a-1 to end 14 a-2,until joined with trusses 12 b of unit cell set 10 b. Ends 14 a-2 havethe same diameter as ends 14 b-1 of trusses 12 b. Trusses 12 b (again,the horizontal trusses) further increase in diameter from ends 14 b-1 toends 14 b-2. TheY- and Z-direction trusses joined at ends 14 a-1 havethe same diameter as ends 14 a-1. The Y-and Z-direction trusses commonto set 10 a and set 10 b have the same diameter as ends 14 a-2 / 14 b-1.TheY- and Z-direction trusses joined at ends 14 b-2 have the samediameter as ends 14 b-2. This configuration provides a continuousdielectric gradient increasing along the X- and Y-axis of polymerstructure 20. The dielectric gradient along the Z-axis is constant.

The direction of the dielectric gradient can accordingly be varied inthe polymer structure by varying the diameter of the trusses in the unitcells accordingly as shown in FIGS. 10A-10F. For example, the dielectricconstant can vary in three dimensions from a common point as shown inFIG. 10A, where the arrows indicate a continuous, uniform decrease indielectric constant in three dimensions from a centerpoint 30 of ahemisphere toward the edges of the hemisphere.

FIG. 10B shows a cross-sectional view of a cylinder dividedlongitudinally into three sections, an inner section, an intermediatesection, and an outer section. The inner section has a first dielectricconstant, the intermediate section has a second dielectric constant, andthe outer section has a third dielectric constant, providing a radial,step gradient dielectric constant. In an aspect, the first dielectricconstant can be lower than the second dielectric constant, which can belower than the third dielectric constant. Alternatively, in anotheraspect, the first dielectric constant can be higher than the seconddielectric constant, which can be higher than the third dielectricconstant. In still another aspect, the first dielectric constant can behigher than the second dielectric constant, and the third dielectricconstant can be higher than the first and second dielectric constants.

FIG. 10C shows a frustoconical shape divided horizontally into sections32, 34, and 36, where the arrow indicates a decrease in dielectricconstant from section 32 to 34 to 36. As shown in another aspect in FIG.10D, sections 42 and 46 can have the same first dielectric constant, andsections 44 and 48 can have the same second dielectric constant, whereineither of the first and second dielectric constants are higher or lowerthan the other, providing a periodic step gradient.

FIG. 10D shows a cubic polymer structure shape divided into sections 42,44, 46, and 48. Sections 42, 46 can have the same first dielectricconstant and sections 44, 48 can have the same second dielectricconstant. The first dielectric constant can be greater than or less thanthe second dielectric constant, which can establish a periodicdielectric constant gradient. It is also possible for the gradient tohave other variations. For example, the gradient can vary randomly orpseudo-randomly from one point of the structure to another.

In another aspect, FIG. 10E shows a cubic polymer structure shape havinga first vertex 52 a and a second vertex 52 b. The dielectric constantcan vary continuously throughout the shape from first vertex 52 a tosecond vertex 52 b. In still another aspect, FIG. 10F shows a cubicpolymer structure shape having a first vertex 52 a and a second vertex52 b. A first section 53, shown in the shape of a cylinder is locatedspanning first vertex 52 a to second vertex 52 b. Second section 54surrounds first section 53. First section 53 can have a first dielectricconstant and second section 54 can have a second dielectric constant,where the first and second dielectric constants differ. It is alsopossible for the dielectric constant of each section to varyindependently. For example, first section 53 can have a dielectricconstant that increases in a step gradient from vertex 52 a to vertex 52b, while section 54 can have a single dielectric constant.

In some aspects, the interstitial spaces of each unit cell (e.g., 13 cin FIGS. 8 and 13 b in FIG. 9 ) are filled with air. In other aspects,the interstitial spaces can be filled by a dielectric material. Suchfilling can be conducted by impregnation of the polymer structure afterit is manufactured. The dielectric material filler can have a lowerdielectric constant than the material used to form at least some of thetrusses. For example, in some aspects the dielectric filler can have avery low dielectric constant (e.g., polytetrafluoroethylene (PTFE)) andbe present to further support the trusses of the polymer structure. Thisallows manufacture of very thin trusses or can provide stiffening tomore flexible trusses. In other aspects, the polymer structure can beformed using a low dielectric constant material, and then filled with ahigher dielectric constant material. This technique can be useful toprovide polymers structures having an overall higher dielectric constantgradient.

As is clear to those of skill in the art from the above discussion, adirection of the dielectric gradient can be varied in any direction byvarying the diameter of a set of trusses in the desired direction.Different shapes of gradients can be manufactured, or even differentshapes of gradients within a single polymer structure. A combination ofstep gradients and continuous gradients can be present, for example afirst section having a step gradient adjacent to a second portion havinga continuous gradient. The particular gradient or combination ofgradients used can be selected based on the end purpose of the polymerstructure.

These complex features can be readily obtained by use of SLA methods,which allow ready manufacture of the desired gradient in any directionand in any shape within the polymer structure. The magnitude of thegradient, i.e., the range, can vary widely, depending on the type ofunit cells, the diameters of the trusses, and the materials used. Forexample, the range of the dielectric constant can be from greater than 1(i.e., greater than the dielectric constant of air) to 20, each measuredat 10 GHz, 50% relative humidity, and 23° C. Any gradient of dielectricconstants within this range can be obtained, for example from 1.1 to 10,or from 1.1 to 5, or 1.1 to 3 across the polymer structure, eachmeasured at 10 GHz, 50% relative humidity, and 23° C. Alternatively, thedielectric constant gradient can be from 5 to 20, or from 5.1 to 18, orfrom 5.1 to 15, or from 5.5 to 11, or from 6 to 10 across the polymerstructure, each measured at 10 GHz, 50% relative humidity, and 23° C.

Specific SLA methods are described, for example, in WO2014/126837. SLAmethods further allow the use of a wide variety of radiation-curableresins to form the polymer structures. The particular radiation-curableresin compositions are selected based on their suitability for use inSLA methods (i.e., can be provided in liquid form), and to provide thedesired mechanical and electrical properties to the polymer structures.The liquid resin composition for forming the polymer structures caninclude a radiation-curable, i.e., a photocurable and/or free radicalcurable monomer component and a photoinitiator component. “Monomer” asused herein is inclusive of photocurable compounds, oligomers,prepolymers, and polymers. “Curable” and “curing” includes polymerizableand crosslinkable, and polymerizing and curing. Suitable monomersinclude radiation-curable groups such as acryl (CH₂═CHCOO—), methacryl(CH₂═C(CH₃)COO), acrylamide (CH₂═CHCONH—, methacrylamide(CH₂═C(CH₃)CONH), vinyl (CH₂═CH—), allyl (CH₂═CH—CH₂—), other alkenessuch as unsaturated aromatic compounds (e.g., styrenics), cyclicalkenes, alkynes,, carbon monoxide, or a combination thereof. Forconvenience, “radiation-curable groups” includes groups curable in thepresence of an initiator that can be photoactivated, such as a cationicphotoinitiator. Such groups include epoxy, vinyl ether, heterocyclicgroups such as lactones, lactams, and cyclic amines, and other groups.The monomer can be linear, branched, cyclic, or crosslinked, and canhave one or more functional groups, for example one or more acryl groups(e.g., a trifunctional acrylate monomer) or one or more vinyl groups(e.g., a divinyl ether). Examples of liquid monomers and initiatorsinclude but are not limited to those set forth in WO2016/153711,US8232043, US8119214, US 7935476, US7767728, US 7649029, WO2012/129968,CN102715751, and JP 2012210408A.

Exemplary monomers and multifunctional monomers include aradiation-curable silicone, a urethane acrylate, a urethanemethacrylate, a (C₁₋₆ alkyl) acrylate, a (C₁₋₆ alkyl) methacrylate suchas methyl methacrylate, a urethane dimethacrylate, 1,3-glyceroldimethacrylate, 1,6-hexanediol diacrylate, 1,6-hexanedioldimethacrylate, 1,4-butanediol diacrylate, 1,4-butanedioldimethacrylate, methylene glycol dimethacrylate, diethylene glycoldivinyl ether, methylene glycol divinyl ether, 1,4-cylcohexanedimethylol divinyl ether, dipropylene glycol divinyl ether, tripropyleneglycol divinyl ether, 1,6-hexanediol divinyl ether, and 1,4-butanedioldivinyl ether, methoxyethene, 4-methoxystyrene, styrene,2-methylprop-1-ene, 1,3-butadiene, oxirane, thietane, tetrahydrofuran,oxazoline, 1,3,-dioxepane, and oxetan-2-one.

The photoinitiator component includes one or more photoinitiators. Forexample, the photoinitiator component can include one or more freeradical photoinitiators or one or more cationic photoinitiators.Photoinitiators known in the art for use in compositions for SLA methodscan be used. Exemplary free radical photoinitiators include a compoundthat produces a free radical on exposure to radiation such asultraviolet and/or visible radiation, in an amount sufficient toinitiate a polymerization reaction. The free-radical photoinitiator canbe a single compound, a mixture of two or more active compounds, or acombination of two or more different compounds (such as co-initiators).

Exemplary cationic photoinitiators include compounds that form aproticacids or Bronsted acids upon exposure to radiation such as ultravioletand/or visible radiation, in an amount sufficient to initiatepolymerization. The cationic photoinitiator used can be a singlecompound, a mixture of two or more active compounds, or a combination oftwo or more different compounds (such as co-initiators). Examples ofcationic photoinitiators include onium salts, sulfonium salts, andiodonium salts, such as diphenyl iodide hexafluorophosphate, diphenyliodide hexafluoroarsenate, diphenyl iodide hexafluoroantimonate,diphenyl p-methoxyphenyl triflate, diphenyl p-toluenyl triflate,diphenyl p-isobutylphenyl triflate, diphenyl p-tert-butylphenyltriflate, triphenylsulfonium hexafluororphosphate, triphenylsulfoniumhexafluoroarsenate, triphenylsulfonium hexafluoroantimonate, andtriphenylsulfonium triflate, dibutylnaphthylsulfonium triflate, asdescribed in US7824839, US7550246, US7534844, and in “PhotoacidGenerator Selection Guide for the electronics industry and energycurable coatings” (BASF 2010). The cationic photoinitiator can be usedin conjunction with a photosensitizer, e.g. 9,10-diethoxyanthracene, toenable the cationic photoinitiator to be activated over a broader rangeof wavelengths.

The radiation-curable resin composition can have additional componentssolubilized therein, including thermally curable resin components,thermal cure initiators, pigments, dyes, flame retardants, antioxidants,plasticizers, polymerization inhibitors, and the like, depending on thepurpose of the polymer structure being fabricated.

In some aspect the radiation-curable resin composition further comprisesa thermally curable resin component and thermal cure initiator componentto initiate thermal cure. Inclusion of a thermally curable resincomponent allows multi-stage curing of the polymer structure.Radiation-curable compositions including a thermally curable resincomponent and a thermal cure initiator component are described, forexample, in WO2017/040883. Examples of monomers that can be used asthermally curable resin components include 1,3-dicyanatobenzene,1,4-dicyanatobenzene, 1,3,5-tricyanatobenzene, 1,3-dicyanatonaphthalene,1,3,6-tricyanatoaphthalene, 2,2′-dicyanatobiphenyl,bis(4-cyanathophenyl) methane, 4-chloro-1,3-dicyanatobenzene, cyanatednovolacs produced by reacting a novolac with cyanogen halide, andcyanated bisphenol polycarbonate oligomers produced by reacting abisphenol polycarbonate oligomer with cyanogen halide. Examples ofthermal cure initiators include peroxides, certain nucleophiliccatalysts, or certain metal catalysts as is known in the art.

The relative amounts of each component of the radiation-curable resincomposition can be, for example, 10 to 95 weight percent (wt%) of theradiation-curable monomer component, 0.11 to 15 wt% of thephotoinitiator component, 0 to 90 wt% of the thermally curable resincomponent, and 0 to 10 wt% of the thermal cure initiator component, eachbased on the total weight of the composition.

A general method for SLA manufacture of a polymer structure having aspatially gradient dielectric constant generally includes providing avolume of the above-described liquid, radiation-curable composition;irradiating a portion of the liquid, radiation-curable composition withactivating radiation in a pattern to form a layer of the polymerstructure on a substrate; contacting the formed layer with the liquid,radiation-curable composition; irradiating a portion of the liquid,radiation-curable composition with activating radiation in a pattern toform a next layer of the polymer structure; and repeating the contactingand the irradiating to form the polymer structure, wherein the polymerstructure comprises a plurality of unit cells, wherein each unit cell isdefined by a plurality of trusses formed by the irradiation, and thetrusses of each unit cell are dimensioned to provide the spatiallygradient dielectric constant. In a preferred aspect, the method is astereolithography method as described, for example, in US9205601.

After the polymer material is manufactured, the 3D-printed polymermaterial can optionally be post-cured, e.g., further photopolymerized.If a thermosetting resin composition is included in theradiation-curable composition, the post-cure can be thermal, for exampleby exposure to heat in an oven. Such dual radiation cure and thermalcure is described, for example, in WO2017/040. Both a radiation and athermal post-cure can be used.

In an aspect, the polymer material is contacted with an electricallyconductive layer. In some aspects, at least two alternating polymerstructures or at least two alternating layers of the electricallyconductive layer are present to form a stack. Useful electricallyconductive materials for the conductive layer include, for example,stainless steel, copper, gold, silver, aluminum, zinc, tin, lead, atransition metal, or a combination thereof. There are no particularlimitations regarding the thickness of the conductive layer, nor arethere any limitations as to the shape, size, or texture of the surfaceof the electrically conductive layer. The conductive layer can have athickness of 1 to 2000 micrometers, or 10 to 1000 micrometers. When twoor more conductive layers are present, the thickness of each layer canbe the same or different. The conductive layer can comprise a copperlayer. Suitable conductive layers include a thin layer of a conductivemetal such as a copper foil presently used in the formation of circuits,for example, electrodeposited copper foils.

The conductive layer can be contacted with the polymer structure byplacing the conductive layer on the platform used for the additivemanufacturing process, and printing onto the conductive layer.Alternatively, the polymer material can be contacted with the conductivelayer by direct laser structuring, or by adhesion. Other methods knownin the art can be used to apply the conductive layer where permitted bythe particular materials and form of the polymer materials, for example,electrodeposition, chemical vapor deposition, and the like.

For example, the conductive layer can be applied by laser directstructuring. Here, the 3D-printed polymer material can comprise a laserdirect structuring additive, and the laser direct structuring cancomprise using a laser to irradiate the surface of the substrate,forming a track of the laser direct structuring additive, and applying aconductive metal to the track. The laser direct structuring additive cancomprise a metal oxide particle (such as titanium oxide and copperchromium oxide). The laser direct structuring additive can comprise aspinel-based inorganic metal oxide particle, such as spinel copper. Themetal oxide particle can be coated, for example, with a compositioncomprising tin and antimony (for example, 50 to 99 wt% of tin and 1 to50 wt% of antimony, based on the total weight of the coating). The laserdirect structuring additive can comprise 2 to 20 parts of the additivebased on 100 parts of the respective composition. The irradiating can beperformed with a YAG laser having a wavelength of 1,064 nanometers underan output power of 10 Watts, a frequency of 80 kilohertz (kHz), and arate of 3 meters per second. The conductive metal can be applied using aplating process in an electroless plating bath comprising, for example,copper.

The conductive layer can be adhesively contacted. In an aspect, thepolymer structure can first be formed by photopolymerization. When athermal cure agent is present in the polymer material composition, thepolymer structure and the electrically conductive layer can be contactedand adhered by thermal cure of the polymer material in the polymerstructure. This technique allows “B-staging” of the polymer structures.It is particularly useful where multilayer structures are desired. Forexample, a plurality of layers of the polymer structures can bemanufactured (B-staged); a stack of alternating polymer layers andconductive layers can be made; and then the stack can be thermally curedto adhere the layers. In other aspects, a polymer structure can bemanufactured (B-staged) in the form of a flat sheet; a conductive layercan be contacted with the flat sheet; the layers can be rolled toprovide a cylinder of alternating polymer sheet and conductive layer;and the roll can be thermally cured to adhere the layers.

Alternatively, or in addition, an adhesion layer can be disposed betweenone or more conductive layers and the polymer material.

The polymer structures can be used as or in an electronic device, forexample as an impedance-matching layer, a dielectric waveguide, a lens,a reflect array, an antenna matching structure, a superstrate, acoupler, a divider, and a dielectric antenna (including dielectricresonant antennas and dielectric rod antennas).

As disclosed herein and with reference to all of the foregoing, and withparticular reference to FIG. 11 , an electronic structure or device 100,in particular an electromagnetic (EM) structure or device, can comprisea first dielectric portion (1DP) 20.1, of any dielectric structure 20disclosed herein, in the form of a dielectric resonator antenna (DRA),for example, and a second dielectric portion (2DP) 20.2, of anydielectric structure 20 disclosed herein, in the form of a dielectriclens, such as a Luneburg lens for example, or any other dielectricelement that forms an electromagnetic (EM) far field beam shaper, forexample; or, a dielectric waveguide, or any other dielectric elementthat forms an EM near field radiation conduit, for example. As disclosedherein, and as will be appreciated by one skilled in the art, the 1DPand the 2DP are distinguishable over each other in that the 1DP isstructurally configured and adapted to have an EM resonant mode thatcoincides with an EM frequency of an electrical signal source that iselectromagnetically coupled to the 1DP, and the 2DP is structurallyconfigured and adapted to: in the case of a dielectric EM far field beamshaper, serve to affect the EM far field radiation pattern originatingfrom the 1DP when excited without itself having a resonant mode thatmatches the EM frequency of the electrical signal source; or, in thecase of a dielectric EM near field radiation conduit, serve to propagatethe EM near field emission originating from the 1DP when excited withlittle or no EM signal loss along the length of the 2DP. As disclosedherein, the phrase electromagnetically coupled is a term of art thatrefers to an intentional transfer of EM energy from one location toanother without necessarily involving physical contact between the twolocations, and in reference to an embodiment disclosed herein moreparticularly refers to an interaction between an electrical signalsource having an EM frequency that coincides with an EM resonant mode ofthe associated 1DP and/or 1DP combined with 2DP. In an embodiment, theelectromagnetically coupled arrangement is selected such that greaterthan 50% of the resonant mode EM energy in the near field is presentwithin the 1DP for a selected operating free space wavelength associatedwith the EM device. In some embodiments, the height H2 of the 2DP isgreater than the height H1 of the 1DP (e.g., the height of the 2DP isgreater than 1.5 times the height of the 1DP, or the height of the 2DPis greater than 2 times the height of the 1DP, or the height of the 2DPis greater than 3 times the height of the 1DP). In some embodiments, theaverage dielectric constant of the 2DP is less than the averagedielectric constant of the 1DP (e.g., the average dielectric constant ofthe 2DP is less than 0.5 the average dielectric constant of the 1DP, orthe average dielectric constant of the 2DP is less than 0.4 the averagedielectric constant of the 1DP, or the average dielectric constant ofthe 2DP is less than 0.3 the average dielectric constant of the 1DP). Insome embodiments, the 2DP has axial symmetry around a specified axis(the z-axis depicted in FIG. 11 for example). In some embodiments, the2DP has axial symmetry around an axis that is normal to an electricalground plane surface 102 on which the 1DP is disposed.

As stated above, the methods described herein allow fast, efficientmanufacture of materials having a preselected dielectric constantgradient, in a variety of configurations and a variety of shapes, with avariety of compositions. The methods have many other advantages,including dramatically reducing the time from design to prototyping tocommercial product. Since no tooling is needed, design changes can bemade quickly. Minimal energy is used, compared to injection molding orother molding processes. Use of additive manufacturing can also decreasethe amount of waste and raw materials. The method can further be used tofacilitate production of geometrically complex parts. The method canfurther reduce the parts inventory for a business since parts can bequickly made on-demand and on-site.

Set forth below are various non-limiting aspects of the disclosure.

Aspect 1: A stereolithography method of manufacture of a polymerstructure having a spatially gradient dielectric constant, the methodcomprising: providing a volume of a liquid, radiation-curablecomposition; irradiating a portion of the liquid, radiation-curablecomposition with activating radiation in a pattern to form a layer ofthe polymer structure; contacting the layer with the liquid,radiation-curable composition; irradiating the liquid, radiation-curablecomposition with activating radiation in a pattern to form a secondlayer on the first layer; and repeating the contacting and irradiatingto form the polymer structure, wherein the polymer structure comprises aplurality of unit cells wherein each unit cell is integrally connectedwith an adjacent unit cell, each unit cell is defined by a plurality oftrusses formed by the irradiation, wherein the trusses are integrallyconnected with each other at their respective ends, and the trusses ofeach unit cell are dimensioned to provide the spatially gradientdielectric constant.

Aspect 2: The method of aspect 1 wherein the unit cell structure is anoctet structure.

Aspect 3a: The method of any one or more of the preceding claims,wherein each of the unit cells can have size less than 30%, or less than20%, or less than 10% of a wavelength of an electromagnetic wave inwhich the polymer structure is operable.

Aspect 3b: The method of any one or more of the preceding aspects,wherein the polymer structure is operable within a wavelength of anelectromagnetic wave in the range from 3 to 300 millimeters.

Aspect 4: The method of any one or more of the preceding aspects,wherein each truss has an average diameter in the range of 0.03 to 5.0millimeter, preferably 0.05 to 4.0 millimeter.

Aspect 5: The method of any one or more of the preceding aspects,wherein the dielectric constant gradient is a step gradient.

Aspect 6: The method of any one or more of the preceding aspects,wherein the dielectric gradient is a continuous gradient.

Aspect 7: The method of any one or more of the preceding aspects,wherein the dielectric gradient has endpoints in a range from 20 togreater than 1, measured at 10 GHz, 23° C., and 50% relative humidity.

Aspect 8: The method of any one or more of the preceding aspects,further comprising impregnating the polymer structure with a dielectricmaterial.

Aspect 9: The method of any one or more of the preceding aspects,wherein the liquid, radiation-curable composition comprises a thermallycurable component, and the method further comprises thermally curing thepolymer structure.

Aspect 10: The method of aspect 9, comprising contacting the polymerstructure with an electrically conductive substrate and thermally curingthe polymer structure.

Aspect 11: The method of aspect 9, further comprising contacting atleast two alternating layers of the polymer structure or at least twolayers of the electrically conductive substrate to form a stack, andthermally curing the polymer structure in the stack.

Aspect 12: The polymer structure having a spatially gradient dielectricconstant formed by any of the preceding aspects.

Aspect 13: An electronic device comprising the polymer structure ofaspect 12, wherein the device is an impedance-matching layer, adielectric waveguide, a lens, a reflect array, an antenna matchingstructure, a superstrate, a coupler, a divider, or a dielectric antenna.

Aspect 14: An electronic device, comprising a polymer structure, whereinthe polymer structure comprises: a unified body of dielectric materialcomprising a plurality of unit cells, each unit cell comprising aplurality of trusses integrally connected with each other at theirrespective ends, wherein each unit cell is integrally connected with anadjacent one of the unit cells; wherein the average dielectric constantof the unified body of dielectric material varies from a portion of thebody to another portion of the body.

Aspect 15: The electronic device of Aspect 13, wherein the plurality oftrusses is integrally connected with each other only at their respectiveends

Aspect 16: The electronic device of any one or more of Aspects 14 to 15wherein each unit cell of the plurality of unit cells has an octetlattice structure.

Aspect 17: The electronic device of any one or more of Aspects 14 to 16,wherein each unit cell of the plurality of unit cells comprisesinterstitial spaces between the plurality of trusses.

Aspect 18: The electronic device of Aspect 17, wherein the interstitialspaces comprise air.

Aspect 19: The electronic device of Aspect 18, wherein the interstitialspaces comprise a dielectric material other than air.

Aspect 20: The electronic device of any one or more of Aspects 14 to 19,wherein the average dielectric constant of the unified body ofdielectric material decreases in a direction from an internal portion ofthe body to an outer portion of the body.

Aspect 21: The electronic device of any one or more of Aspects 14 to 19,wherein the average dielectric constant of the unified body ofdielectric material varies periodically from a first portion of the bodyto a second portion of the body.

Aspect 22: The electronic device of any one or more of Aspects 14 to 21,wherein the plurality of trusses of a given unit cell have a constantcross-sectional dimension.

Aspect 23: The electronic device of any one or more of Aspects 14 to 21,wherein the plurality of trusses of a given unit cell have anon-constant cross-sectional dimension.

Aspect 24: The electronic device of any one or more of Aspects 14 to 22,wherein the cross-sectional dimension is a circular cross-sectionaldimension.

Aspect 25: The electronic device of Aspects 22 to 24, wherein thenon-constant cross-sectional dimension decreases in a direction from aninternal portion of the body to an outer portion of the body.

Aspect 26: The electronic device of any one or more of Aspects 14 to 25,wherein each truss of the plurality of trusses has an overall maximumcross-sectional dimension in the range of 0.03 to 5.0 millimeters.

Aspect 27: The electronic device of any one or more of Aspects 14 to 26,wherein the spatially gradient dielectric constant of the unified bodyof dielectric material is from 20 to greater than 1, measured at 10 GHz,23° C., and 50% relative humidity.

Aspect 28: The electronic device of any one or more of Aspects 14 to 27,further comprising at least one electrical conductor disposed in contactwith the unified body of dielectric material.

Aspect 29: The electronic device of Aspect 28 wherein the at least oneelectrical conductor is adhered to the unified body of dielectricmaterial via an adhesive material.

Aspect 30: The electronic device of any one or more of Aspects 14 to 29,wherein the unified body of dielectric material forms at least part ofan impedance-matching layer, a dielectric waveguide, a lens, a reflectarray, an antenna matching structure, a superstrate, a coupler, adivider, or a dielectric antenna.

Aspect 31: The electronic device of Aspect 30, wherein the unified bodyof dielectric material is a first dielectric portion, 1DP, of theelectronic device, and further comprising a second dielectric portion,2DP, wherein: the 1DP has a proximal end and a distal end; the 2DP has aproximal end and a distal end; and the proximal end of the 2DP isdisposed proximate the distal end of the 1DP.

Aspect 32: The electronic device of Aspect 31, further comprising anelectrical ground plane surface upon which the 1DP is disposed.

Aspect 33: The electronic device of any one or more of Aspects 31 to 33,wherein a height H2 of the 2DP is greater than a height H1 of the 1DP.

The compositions, methods, and articles can alternatively comprise,consist of, or consist essentially of, any appropriate materials, steps,or components herein disclosed. The compositions, methods, and articlescan additionally, or alternatively, be formulated so as to be devoid, orsubstantially free, of any materials (or species), steps, or components,that are otherwise not necessary to the achievement of the function orobjectives of the compositions, methods, and articles.

The terms “a” and “an” do not denote a limitation of quantity, butrather denote the presence of at least one of the referenced item. Theterm “or” means “and/or” unless clearly indicated otherwise by context.The term “combination” is inclusive of blends, mixtures, alloys,reaction products, and the like. Also, “at least one of” means that thelist is inclusive of each element individually, as well as combinationsof two or more elements of the list, and combinations of at least oneelement of the list with like elements not named. Similarly, “acombination thereof” is open, and can include at least one of the namedelements, optionally together with a like or equivalent element notnamed.

The endpoints of all ranges directed to the same component or propertyare inclusive of the endpoints, are independently combinable, andinclude all intermediate points and ranges. For example, ranges of “upto 25 wt%, or 5 to 20 wt%” is inclusive of the endpoints and allintermediate values of the ranges of “5 to 25 wt%,” such as 10 to 23wt%, and the like.

When an element such as a layer, film, region, or substrate is referredto “contacting” or as being “on” another element, it can be directlycontacting or directly on the other element or intervening elements canalso be present. In contrast, when an element is referred to as“directly contacting” or as being “directly on” another element, thereare no intervening elements present. Although the terms first, second,third etc. may be used herein to describe various elements, components,regions, layers, or sections, these elements, components, regions,layers, or sections should not be limited by these terms. These termsare only used to distinguish one element, component, aspect, region,layer, or section from another element, component, region, layer, orsection. Thus, a first element, component, region, layer, or sectiondiscussed below could be termed a second element, component, region,layer, or section without departing from the teachings of the presentaspects.

Exemplary aspects are described herein with reference to cross sectionillustrations that are schematic illustrations. As such, variations fromthe shapes of the illustrations as a result, for example, ofmanufacturing techniques and/or tolerances, are to be expected. Thus,aspects described herein should not be construed as limited to theparticular shapes or relative sizes of regions as illustrated herein butare to include deviations in shapes that result, for example, frommanufacturing or design. For example, a region illustrated or describedas flat may, typically, have rough and/or nonlinear features. Moreover,sharp angles that are illustrated may be rounded. Thus, the regionsillustrated in the figures are schematic in nature and their shapes arenot intended to illustrate the precise shape or relative size of aregion and are not intended to limit the scope of the present claims

Unless specified to the contrary herein, all test standards are the mostrecent standard in effect as of the filing date of this application, or,if priority is claimed, the filing date of the earliest priorityapplication in which the test standard appears.

Unless defined otherwise, technical and scientific terms used hereinhave the same meaning as is commonly understood by one of skill in theart to which this invention belongs. All cited patents, patentapplications, and other references are incorporated herein by referencein their entirety. However, if a term in the present applicationcontradicts or conflicts with a term in the incorporated reference, theterm from the present application takes precedence over the conflictingterm from the incorporated reference.

While particular embodiments have been described, alternatives,modifications, variations, improvements, and substantial equivalentsthat are or can be presently unforeseen can arise to applicants orothers skilled in the art. Accordingly, the appended claims as filed andas they can be amended are intended to embrace all such alternatives,modifications variations, improvements, and substantial equivalents.

What is claimed is:
 1. A stereolithography method of manufacture of apolymer structure having a spatially gradient dielectric constant, themethod comprising: providing a volume of a liquid, radiation-curablecomposition; irradiating a portion of the liquid, radiation-curablecomposition with activating radiation in a pattern to form a layer ofthe polymer structure; contacting the layer with the liquid,radiation-curable composition; irradiating the liquid, radiation-curablecomposition with activating radiation in a pattern to form a secondlayer on the first layer; and repeating the contacting and irradiatingto form the polymer structure, wherein the polymer structure comprisesan open-lattice cell structure comprising a plurality of unit cellswherein each unit cell is integrally connected with an adjacent unitcell, and wherein density of the polymer structure is varied to providethe spatially gradient dielectric constant.
 2. The method of claim 1,wherein the gradient is a step gradient.
 3. The method of claim 1,wherein the gradient is a continuous gradient, a random gradient, or apseudo-random gradient.
 4. The method of claim 1, wherein the spatiallygradient dielectric constant has endpoints in a range from 20 to greaterthan 1, measured at 10 GHz, 23° C., and 50% relative humidity.
 5. Themethod of claim 1, wherein the spatially gradient dielectric constanthas endpoints in a range from 10 to greater than 1, measured at 10 GHz,23° C., and 50% relative humidity.
 6. The method of claim 1, wherein thespatially gradient dielectric constant has endpoints in a range from 5to greater than 1, measured at 10 GHz, 23° C., and 50% relativehumidity.
 7. The method of claim 1, further comprising impregnating thepolymer structure with a dielectric material other than air.
 8. Themethod of claim 1, wherein the liquid, radiation-curable compositioncomprises a thermally curable component, and the method furthercomprises thermally curing the polymer structure.
 9. The method of claim8, comprising contacting the polymer structure with an electricallyconductive substrate and thermally curing the polymer structure.
 10. Themethod of claim 8, further comprising contacting at least twoalternating layers of the polymer structure or at least two layers ofthe electrically conductive substrate to form a stack, and thermallycuring the polymer structure in the stack.
 11. The method of claim 1,wherein in the polymer structure, an average dielectric constant of thepolymer structure decreases in a direction from an internal portion ofthe polymer structure to an outer portion of the polymer structure. 12.The method of claim 11, wherein the average dielectric constant of thepolymer structure varies periodically from a first portion of the bodyto a second portion of the body.
 13. The method of claim 1, wherein anaverage dielectric constant of the polymer structure varies periodicallyfrom a first portion of the body to a second portion of the body. 14.The method of claim 1, wherein at least one electrical conductor isdisposed in contact with the polymer structure.
 15. A stereolithographymethod of manufacture of a polymer structure having a spatially gradientdielectric constant, the method comprising: providing a volume of aliquid, radiation-curable and thermally-curable composition; irradiatinga portion of the liquid, radiation-curable and thermally curablecomposition with activating radiation in a pattern to form a layer ofthe polymer structure; contacting the layer with the liquid,radiation-curable and thermally curable composition; irradiating theliquid, radiation-curable composition with activating radiation in apattern to form a second layer on the first layer; and repeating thecontacting and irradiating to form the polymer structure; and thermallycuring the polymer structure; wherein the polymer structure comprises anopen-lattice cell structure comprising a plurality of unit cells whereineach unit cell is integrally connected with an adjacent unit cell,wherein density of the polymer structure is varied to provide thespatially gradient dielectric constant, and wherein the spatiallygradient dielectric constant has endpoints in a range from 10 to greaterthan 1, measured at 10 GHz, 23° C., and 50% relative humidity.
 16. Themethod of claim 15, further comprising contacting the polymer structurewith an electrically conductive substrate, followed by thermally curingthe polymer structure.
 17. The method of claim 15, wherein thedielectric gradient has endpoints in a range from 5 to greater than 1,measured at 10 GHz, 23° C., and 50% relative humidity.
 18. Astereolithography method of manufacture of a polymer structure having aspatially gradient dielectric constant, the method comprising: providinga volume of a liquid, radiation-curable composition; irradiating aportion of the liquid, radiation-curable composition with activatingradiation in a pattern to form a layer of the polymer structure;contacting the layer with the liquid, radiation-curable composition;irradiating the liquid, radiation-curable composition with activatingradiation in a pattern to form a second layer on the first layer; andrepeating the contacting and irradiating to form the polymer structure,wherein the polymer structure comprises an open-lattice cell structurecomprising a plurality of unit cells wherein each unit cell isintegrally connected with an adjacent unit cell, each unit cell has sizeof less than 30% of a wavelength of an electromagnetic wave in which thepolymer structure is operable, wherein density of the polymer structureis varied to provide the spatially gradient dielectric constant, andwherein the spatially gradient dielectric constant of the polymerstructure has endpoints in a range from 10 to greater than 1, measuredat 10 GHz, 23° C., and 50% relative humidity.
 19. The method of claim18, wherein the dielectric gradient has endpoints in a range from 5 togreater than 1, measured at 10 GHz, 23° C., and 50% relative humidity.